Abstract. In 2010, Davvaz and Mirvakili [6] defined the concept of Krasner -hyperring, defined a fundamental relation on the structure and proved the isomorphism theorems where the hyper ideals considered in the construction of its quotient class is not necessarily normal. Recently, Castillo and Vilela [#!CAS!#] considered a particular case where and called a Krasner ternary hyperring and proved the isomorphism theorems without the normality condition. In this article, regularity is defined in Krasner ternary hyperrings and proved that this property is radical in these classes of algebraic hyperstructure.